\begin{problem}{Neighbours}{nei.in}{nei.out}{10 seconds}{64 megabytes}

  The area of the Great Bytean Mountains can be imagined
  as a rectangle in a plane with cartesian coordinate system.
  This rectangle has two opposite vertices in points $(0,0)$ and $(w,h)$,
  where $w$ and $h$ are positive integers.
  There are $n$ major peaks in the mountains, each of which is located
  in one grid point of the rectangle (a grid point is a point having
  integer coordinates).
  More and more tourists discover the beauty of Great Bytean Mountains
  and everyone would like to build a house there.
  The rules of Great Bytean Mountain Park are very strict though:
  in each grid point of the rectangle at most one house can be built
  and moreover there cannot be any house on the peak of any mountain.
  So there are $(w+1)\cdot (h+1)-n$ possible locations of houses.

  Some of the locations are considered better than other.
  We say that a grid point $(x,y)$ has a northern neighbour if there
  is a mountain peak at some point $(x,y+d)$, where $d$ is a positive integer.
  Similarly, southern, eastern and western neighbours could be defined.
  In this way, every grid point that is not a mountain peak
  may have between $0$ and $4$ neighbours --- the more neighbours,
  the better is the location (because of a better view of the mountains).
  The director of Great Bytean Mountain Park would like to know
  the maximal profit that can be achieved by selling locations to tourists.
  Help him and count how many grid points in the mountains (excluding
  mountain peaks) have $0$, $1$, $2$, $3$ and $4$ neighbours.

    Write a program which:
    \begin{itemize}
      \item
        reads the description of Great Bytean Mountains from the standard
        input,
      \item
        counts the numbers of grid points, having $0$, $1$, $2$, $3$ and $4$
        neighbours,
      \item
        writes the result to the standard output.
    \end{itemize}

\InputFile
  The first line of input contains three integers $w$, $h$ and $n$
  ($1\le w,h\le 10^9$, $1\le n\le 500\,000$), separated by single spaces.
  The following $n$ lines contain the descriptions of locations of
  mountain peaks in the park.
  Each of them contains two integers $x$ and $y$
  ($0\le x\le w$, $0\le y\le h$), separated by a single space.
  All peaks are in distinct locations.


\OutputFile

  The first and only line of output should contain $5$ integers,
  separated by single spaces and denoting the numbers of grid
  points (excluding peaks), having exactly $0$, $1$, $2$, $3$ and $4$
  neighbours.
   

\Example

\begin{example}
\exmp{
4 3 6
0 3
2 3
2 1
0 1
3 2
1 2
}{
1 7 2 3 1
}%
\end{example}

\includegraphics[width=7cm]{neizad1.eps}

  Points having two neighbours are: $(3,1)$ and $(3,3)$,
  points with three neighbours are: $(1,1)$, $(0,2)$ and $(1,3)$.
  Point $(2,2)$ has four neighbours, point $(4,0)$ does not
  have any neighbours and all remaining points have exactly one
  neighbour each.
\end{problem}
